KokkosLapack::svd

Defined in header: KokkosLapack_svd.hpp

template <class ExecutionSpace, class AMatrix, class SVector, class UMatrix, class VMatrix>
void svd(const ExecutionSpace& space, const char jobu[], const char jobvt[], const AMatrix& A,
         const SVector& S, const UMatrix& U, const VMatrix& Vt);

template <class AMatrix, class SVector, class UMatrix, class VMatrix>
void svd(const char jobu[], const char jobvt[], const AMatrix& A,
         const SVector& S, const UMatrix& U, const VMatrix& Vt);

Compute the singular value decomposition of matrix A which can be written as

\[A=U*S*transpose(V)\]

Note

The function will compute the transpose of the right singular vectors Vt for computational efficiency.

  1. Compute the singular value decomposition of A into S, U and Vt using the resources associated with space.

  2. Same as 1. but using the resources associated with AMatrix::execution_space().

Parameters

space:

execution space instance.

jobu, jobvt:

characters used to control the calculation of left (jobu) and right (jobvt) singular vectors. A means all the singular vectors are computed, S means the first \(min(m, n)\) vectors will be computed in U, O means the first \(min(m, n)\) vectors will be computed and overwritten in A, N means no singular vectors will be computed.

A:

the matrix on which the singular value decomposition will be computed.

S:

the min(m, n) singular values of A in decreasing order.

U, Vt:

the left and right singular vectors of A computed according to the jobu and jobvt flags.

Type Requirements

  • ExecutionSpace must be a Kokkos execution space

  • the three matrix types AMatrix, UMatrix and VMatrix have the same requirements:

    • Kokkos::is_view_v<AMatrix> && AMatrix::rank() == 2 && Kokkos::SpaceAccessibility<ExecutionSpace, typename AMatrix::memory_space>::accessible

    • Kokkos::is_view_v<UMatrix> && UMatrix::rank() == 2 && Kokkos::SpaceAccessibility<ExecutionSpace, typename UMatrix::memory_space>::accessible

    • Kokkos::is_view_v<VMatrix> && VMatrix::rank() == 2 && Kokkos::SpaceAccessibility<ExecutionSpace, typename VMatrix::memory_space>::accessible

  • the vector of singular values has the following requirements:

    • Kokkos::is_view_v<SVector> && SVector::rank() == 1 && Kokkos::SpaceAccessibility<ExecutionSpace, typename SVector::memory_space>::accessible

    • std::is_same_v<typename SVector::array_layout, Kokkos::LayoutStride> && S.span_is_contiguous() only contiguous strided spans are allowed.

Note

Should check that the ouput view SVector, UMatrix and VMatrix are storing non-const data.

Example